A visualization tool for material property anisotropy: representational surfaces of 3rd-rank tensors

The representational surface has become an effective means for expressing the anisotropy in piezoelectric single crystals and textured polycrystalline materials. Although the mathematics involved with such a representation can be taught at the graduate level, the knowledge and familiarity necessary to represent these surfaces graphically makes such representations inaccessible to some undergraduate and graduate students. This paper presents a simple, user-friendly tool for generating such representations for 3rd-rank tensors and demonstrates their application to a specific piezoelectric composition. The tool is accessed as a graphical user interface within a commercial mathematical software package.